I. Core concept: The essential boundary between the number of non - conformities and the number of non - conforming products
In the quality inspection system, the number of non - conformities and the number of non - conforming products are two statistical indicators with completely different underlying logics. The core difference lies in the dimension of the counting objects:
Number of non-conformities: The number of items of a certain type of quality defect, that is, the total quantity of this type of non-conformity among all products (for example: how many points of non-conformities of Type A are there).
Number of non-conforming products: The "number of products" containing a certain type of quality defect, that is, how many products have this type of non-conformity (for example, how many products "have" Class A non-conformity, regardless of how many instances there are).
In short: A product may have 5 non-conformities of Class A (counted as 5 non-conformity numbers of Class A), but it is only counted as 1 non-conforming product number of Class A; 10 products each have 1 non-conformity of Class A (counted as 10 non-conformity numbers of Class A and 10 non-conforming product numbers of Class A). The distinction between the two is the basis for subsequent calculation of non-conforming product rate and sampling judgment.
II. Example 1: Workshop part sampling - from "distribution" to "counting"
A certain workshop sampled 1,000 parts for inspection. The distribution of unqualified parts is as follows:
- Five products only contain non-conformities of Class A.
- Four products only contain Class B non-conformities.
- Two products are simultaneously non - compliant with both Category A and Category B.
- Three products are simultaneously non - compliant with both Class B and Class C requirements.
- Five products only contain Class C non-conformities.
1. Category A indicators: The superposition of the number of items and the number of products
Number of Class A non - conformities: The sum of all Class A non - conformities = 5 items that are only of Class A + 2 items in Class A + B (each of these 2 products has 1 Class A non - conformity) = 7;
Number of Class A non-conforming products: The quantity of all products containing Class A non-conformities = 5 products with only Class A non-conformities + 2 products with both Class A and Class B non-conformities = 7 (As long as a product has a Class A non-conformity, regardless of whether it has other classes of non-conformities, it is counted as a Class A non-conforming product).
Nonconforming product rate of Class A: Number of nonconforming products of Class A / Total samples = 7/1000 (reflecting the proportion of products with Class A problems);
Number of Class A non - conformities per 100 units: (Number of Class A non - conformities / Total samples) × 100 = 0.7 (reflecting how many Class A defect points there are on average in every 100 products).
2. Category B indicators: The key to avoiding double counting
Number of non-conformities of Class B: The sum of all non-conformity items of Class B = 4 items of only Class B + 2 items of Class A + Class B + 3 items of Class B + Class C = 9;
Number of Class B non-conforming products: The quantity of all products containing Class B non-conformities = 4 products with only Class B non-conformities + 3 products with both Class B and Class C non-conformities = 7 (The 2 products with both Class A and Class B non-conformities have been counted in the Class A non-conforming products. Here, only the "total number of products containing Class B non-conformities" is counted without double - counting).
Nonconforming product rate of Class B: 7/1000;
Number of Class B non - conformities per 100 units: 0.9.
3. Category C indicators: Focus on the purity of the "self-related" type
Number of Class C non - conformities: The sum of all Class C non - conformities = 3 items of Class B + C + 5 items of only Class C = 8;
Number of Class C non-conforming products: The quantity of all products containing Class C non-conformities = 5 products with only Class C non-conformities (The 3 products with both Class B and Class C non-conformities have been counted as Class B non-conforming products. Here, only the "total number of products containing Class C non-conformities" is counted).
Class C nonconforming product rate: 5/1000;
Number of Class C non-conformities per 100 units: 0.8.
Conclusion of Example 1
Total number of non-conformities (A + B + C) = 7 + 9 + 8 = 24 (the sum of all defect points); Total number of non-conforming products = 7 + 7 + 5 = 19 (the total number of products with defects).
III. Example 2: Multi-Characteristic Products - Counting Rules in Complex Scenarios
A certain product has 5 quality characteristics, which are divided into three categories according to their importance: A (critical), B (secondary), and C (general). After a full inspection of 2,000 pieces, 5 non - conforming products were found, and the specific distribution is as follows:
- Product 3: 1A, 0B, 2C;
- Product 7: 0A, 1B, 1C;
- Product 12: 1A, 1B, 0C;
- Product 19: 0A, 1B, 2C;
- Product: 0A, 0B, 3C at 20:00.20020:00
1. Category A: Precise counting of critical characteristics
Number of Class A non - conformities: 1 Class A of Product 3 + 1 Class A of Product 12 = 2 (only count Class A defect points);
Number of Class A non-conforming products: Product 3 + Product 12 = 2 (only products containing Class A defects are counted);
Class A nonconforming product rate: 2/2000;
Number of non-conformities of Class A per 100 units: 0.1.
2. Category B: Range statistics of secondary characteristics
Number of Class B non-conformities: 1 Class B defect of Product 7 + 1 Class B defect of Product 12 + 1 Class B defect of Product 19 = 3 (total number of Class B defect points);
Number of Class B non-conforming products: Product 7 + Product 12 + Product 19 = 3? No. According to the original text, when counted as products containing only Class B, it is 2 (possibly Products 7 and 19). The core is the number of products containing Class B rather than the number of products containing only Class B — the key here is the number of products rather than the number of pure Class B products.
Non-conforming product rate of Class B: 2/2000;
Number of Class B non - conformities per 100 units: 0.15.
3. Category C: Density statistics of general characteristics
Number of Class C non - conformities: 2C of Product 3 + 1C of Product 7 + 2C of Product 19 + 3C of Product 20 = 8 (Total number of Class C defect points);
Number of Class C non-conforming products: Product 20 = 1 (Only products with Class C defects are counted. The original text counted "products with multiple Class C defects").
Rate of Class C non-conforming products: 1/2000;
Number of Class C non-conformities per 100 units: 0.4.
Conclusion of Example 2
Total number of non-conformities = 2 + 3 + 8 = 13 (all defect points); Total number of non-conforming products = 2 + 2 + 1 = 5 (all products with defects).
IV. Example 3: Sampling Judgment—Implementation from Counting to Decision-Making
For a certain batch of products, the batch size N = 1000, the inspection level IL = II (medium strictness), the AQL for Class A (serious) defects is 1.0 (a maximum of 1 serious non - conforming product per 100 products), and the AQL for Class B (minor) defects is 4.0 (a maximum of 4 minor non - conforming products per 100 products). Sampling revealed that:
- 1 product: 2A + 1B;
- 2 products: 1A + 1B each;
- 1 product: 2B.
Step 1: Calculate the core indicators of Class A/B
Number of Class A non - conformities: 1×2 (Point A of the first product) + 2×1 (Point A of two products) + 1×0 (The last product has no A) = 4 (Total number of Class A defect points);
Number of non-conforming products of Class A: 1 (the first product) + 2 (two products) = 3 (total number of products with Class A defects);
Number of Class B non - conformities: 1×1 (Point B of the first product) + 2×1 (Point B of two products) + 1×2 (Point B of the last product) = 5 (Total number of Class B defect points);
Number of non-conforming products of Class B: 1 (the last product, containing only Class B defects) (total number of products with Class B defects).
Step 2: Rule matching of the sampling plan
The core of sampling judgment is to compare the indicators with the "acceptance number (Ac)" and "rejection number (Re)" corresponding to AQL:
1. Find the sampling code: N = 1000 + IL = II → Code "J";
2. Check Ac/Re:
- Class A (AQL = 1.0 + Code J): Sampling quantity n = 80, Ac = 2 (At most 2 seriously non - conforming products can be accepted), Re = 3 (Reject if the number exceeds).
- Class B (AQL = 4.0 + Code J): Sampling quantity n = 80, Ac = 7 (Maximum 7 slightly non-conforming products are acceptable), Re = 8.
Step 3: Final decision
Class A judgment: Number of non-conforming products = 3 = Re = 3 → Reject;
Category B judgment: Number of non-conforming products = 1
The entire batch is non - acceptable as it triggers rejection due to Class A (serious defects).
Supplementary: The result judged by the "number of non-conforming items"
If the judgment is required to be made based on "defect points" (number of non - conformities) rather than "products" (number of non - conforming products):
- Number of non-conformities of Class A = 4
- Number of non-conformities of Class B = 5
Consistent conclusion: Reject the whole batch.
The application boundaries of two indicators
The distinction between the number of non - conformities and the number of non - conforming products essentially lies in the difference between "defect density" and "defect scope":
- When it is necessary to evaluate "how dense the defects are" (such as the number of scratches on the chip surface), use the number of non - conformities.
- When it is necessary to evaluate "how much of the product is covered by defects" (such as the defective rate of a batch of mobile phones), use the number of non - conforming products.
- In the sampling judgment, critical defects (Class A) are usually judged by the "number of non-conforming products" (focusing on the proportion of problematic products), while minor defects (Class B) can be judged by the "number of non-conformities" (focusing on the density of defect points).
Understanding the boundary between the two is a crucial step for quality statistics to move from "data" to "decision-making".